Abstract
This letter investigates the ergodic secrecy rate (ESR) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence multiple eavesdroppers (Eves), and by assuming discrete phase shifts at the RIS. In particular, a closed-form approximation of the ESR is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS N is large. Asymptotic analysis is provided to investigate the impact of N on the ESR, and it is proved that the ESR scales with log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> N for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.
Highlights
Reconfigurable intelligent surfaces (RISs) utilize a large number of passive reflecting elements to customize wireless communication environments [1]–[4]
The key idea behind the optimization problems in the existing works [9]–[12] lies in achieving a favorable trade-off between these two design objectives, which requires the knowledge of the instantaneous eavesdropping channel state information (CSI) at the transmitter and RIS
We assume that the RIS does not have access to the instantaneous eavesdropping CSI, so that it cannot design φn in order to suppress the received SNRs at the Eves
Summary
Reconfigurable intelligent surfaces (RISs) utilize a large number of passive reflecting elements to customize wireless communication environments [1]–[4]. There exist two objectives for the design of the phase shifts at the RIS: (i) to strengthen the legitimate channels by co-phasing the reflected signals with the signal directly received from the transmitter; and (ii) to suppress the eavesdropping channels by setting the reflected signals at the eavesdroppers (Eves). The authors of [13] proposed a joint beamforming and jamming scheme to enhance the secrecy rate, and the authors of [14] analyzed the secrecy outage probability at the RIS These two works only considered a single eavesdropper and assumed continuous phase shifts at the reflecting elements of the RIS. Notation: C and Z denote the complex domain and integer set, respectively; for brevity, we denote [1 : M ] {1, . . . , M }, where M is a positive integer, and [x]+ max{0, x}; CN denotes the complex Gaussian distributions; E[·] denotes the expectation of a random variable; log(·) and ln(·) denote the base-two and natural logarithms, respectively; and κ is Euler’s constant
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